Question

In figure, $\Delta ABC$ is an equilateral triangle. Points $f,D$ and $E$ are midpoints of side $AB$, side $BC$, side $AC$ respectively. Show that $\Delta FED$ is an equilateral triangle.

Answer 1

$EF||BC$

By basic proportionality theorm ,

$\Delta AFE\sim \Delta ABC$

Similarly ,

$\Delta FBD\sim \Delta ABC\Delta ECD\sim \Delta ACB$

Att point $D$

$\angle BDF+\angle FDE+\angle EDC=18060+\angle FDE+60=180\angle FDE={60}^{\circ }$

Similarly,

$\angle DEF=\angle DFE={60}^{\circ }$

Hence $\Delta DEF$ is equilateral triangle.